Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| isoclinism | isoclinic class of C5⋊#6057 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C5 |
| direct product | C2×C5⋊#6057 |
| unambiguous semidirect product | (C2×C5)⋊#6057 |
| Fitting, socle | C2×C53 ⋊ Q8 |
| Sylow | C53 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C5⋊#6057 |
| commutator, cosocle | C5×C5⋊D5 | C23 |
| Frattini | C1 | G |
| Fitting, socle | C2×C53 | Q8 |
| prime radical | C2×C5×C5⋊D5 | C22 |
| hypocenter | C53 | C2×Q8 |
| LCS | G ▷ C5×C5⋊D5 ▷ C53 | |
| UCS | C1 ◁ C2 | |
136 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
56 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 945);